The graphic row for polygon shows the various geometry methods - check out RECTANGLE_BY_WIDTH, RECTANGLE_BY_AREA, and ENVELOPE.

Also, there's the convex hull property 'getHullRectangle' --- gives you a space-delimited coordinate pair string of the vertices. You can use the distance formula to back out the height/width if not oriented 'orthogonally' to the x/y axes.

Here's some v10.1+ code that calculates an "aspect ratio" in regards to a poly or line FC's hull rectangle (not the same as extent rectangle BTW)... The variables "distance1" and "distance2" are length and width (depending on which one is the longer distance):